Does not having a PS Plus membership affect its cross-play support?

No. As long as you have a PlayStation Network account and access to the internet — which is needed to play Dauntless to begin with — you can choose to opt into its cross-play functionality. This means that regardless of whether or not you have a PlayStation Plus membership, you can play with others who are on Xbox One and PC.

Why does my friend on Xbox One need Xbox Live Gold then?

Microsoft and Sony's policies differ in this regard. While Sony usually allows anyone to play online multiplayer in free-to-play games without needing a PS Plus subscription, Microsoft requires players to have Xbox Live Gold if they want to play online multiplayer, no matter if the game is free-to-play or not.

Does PS Plus offer any benefits in Dauntless?

Yes and no. PlayStation Plus members do get benefits in the form of a free weapon skins pack, but you won't be getting anything that could greatly impact your power level or anything like that. These are purely cosmetic items and don't serve to buff your character. Right now the free Dauntless Model P Weapon Pack contains:

Ostian Chain Blades (Model P)

Ostian Repeaters (Model P)

Ostian Falchion (Model P)

Ostian War Axe (Model P)

Ostian War Hammer (Model P)

Ostian War Pike (Model P)

PlayStation Plus members do sometimes get a better discount while sales are going on — generally 10% more off compared to those who are not members — but no such sales are currently running on any of Dauntless add-ons or currency packs.

Do these free add-ons with PS Plus ever change?

It's too soon to tell for Dauntless, but if it follows in the footsteps of other free-to-play games like Apex Legends and Fortnite, then yes. These free add-on packs for PlayStation Plus members do change up from time to time, so you can likely expect different weapons skins and cosmetics to be included in the future.

Is it worth picking up a PS Plus membership for?

I wouldn't pick up a PlayStation Plus membership just for Dauntless, but it is a subscription that you should still consider for its other benefits. It's hard to pass up when being a member snags you two free games every month.